Problem: Rewrite as a simplified fraction. ${0.\overline{30} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 30.303...\\ 1x &= 0.303...\end{align*}}$ Subtracting the two equations, we have: ${99x = 30}$ ${x = \dfrac{30}{99}} $ ${x = \dfrac{10}{33}} $